View source for Amount of substance

{{Short description|Ratio of the number of particles in a sample to Avogadro's constant}}
{{Infobox physical quantity
| name = Amount of substance
| image = Mole_carbon-12_diagram.svg
| imagesize = 350px
| caption = Approximately 1 [[Mole (unit)|mol]] amount of substance based on 12 grams of carbon-12
| unit = [[Mole (unit)|mol]]
| symbols = {{mvar|n}}
| dimension = wikidata
}}

In [[chemistry]], the '''amount of substance''' (symbol {{mvar|n}}) in a given sample of [[matter]] is defined as a ratio ({{math|1=''n'' = ''N''/''N''<sub>A</sub>}}) between the [[particle number|number]] of [[elementary entities]] ({{mvar|N}}) and the [[Avogadro constant]] ({{math|''N''<sub>A</sub>}}). Since 2019, the value of the Avogadro constant {{math|''N''<sub>A</sub>}} is defined to be exactly {{physconst|NA|ref=no}}. The elementary entities are usually [[molecules]], [[atom]]s, [[ion]]s, or ion pairs of a specified kind. The particular [[chemical substance|substance]] sampled may be specified using a subscript, e.g., the amount of [[sodium chloride]] (NaCl) would be denoted as {{math|''n''<sub>NaCl</sub>}}. The unit of amount of substance in the [[International System of Units]] is the [[Mole (unit)|mole]] (symbol: mol), a [[SI base unit|base unit]].<ref name="bipm9th">{{SIbrochure9th}} p. 134</ref>  Sometimes, the amount of substance is referred to as the '''chemical amount''' or, informally, as the "'''number of moles'''" in a given sample of matter.

== Usage ==
Historically, the mole was defined as the amount of substance in 12&nbsp;grams of the [[Carbon-12|carbon-12 isotope]]. As a consequence, the mass of one mole of a [[chemical compound]], in [[gram]]s, is numerically equal (for all practical purposes) to the mass of one molecule or formula unit of the compound, in [[dalton (unit)|dalton]]s, and the molar mass of an isotope in grams per mole is approximately equal to the mass number (historically exact for carbon-12 with a molar mass of 12 g/mol). For example, a molecule of water has a mass of about 18.015&nbsp;daltons on average, whereas a mole of water (which contains {{physconst|NA|unit=no|ref=no}} water molecules) has a total mass of about 18.015&nbsp;grams.

In chemistry, because of the [[law of multiple proportions]], it is often much more convenient to work with amounts of substances (that is, number of moles or of molecules) than with masses (grams) or volumes (liters).  For example, the chemical fact "1&nbsp;molecule of [[oxygen]] ({{chem|O|2}}) will react with 2 molecules of [[hydrogen]] ({{chem|H|2}}) to make 2 molecules of water ({{chem2|H2O}})" can also be stated as "1 mole of {{chem2|O2}} will react with 2 moles of {{chem2|H2}} to form 2 moles of water". The same chemical fact, expressed in terms of masses, would be "32&nbsp;g  (1 mole) of oxygen  will react with approximately 4.0304&nbsp;g (2 moles of {{chem|H|2}}) hydrogen to make approximately 36.0304&nbsp;g (2 moles) of water" (and the numbers would depend on the [[isotope|isotopic composition]] of the reagents). In terms of volume, the numbers would depend on the pressure and temperature of the [[reagent]]s and [[Product (chemistry)|products]].  For the same reasons, the concentrations of reagents and products in solution are often specified in moles per liter, rather than grams per liter.

The amount of substance is also a convenient concept in [[thermodynamics]].  For example, the pressure of a certain quantity of a [[noble gas]] in a recipient of a given volume, at a given temperature, is directly related to the number of molecules in the gas (through the [[ideal gas law]]), not to its mass.

This technical sense of the term "amount of substance" should not be confused with the general sense of "amount" in the [[English language]]. The latter may refer to other measurements such as mass or volume,<ref name="Giunta">{{cite journal |doi=10.1021/acs.jchemed.5b00690|title=What's in a Name? Amount of Substance, Chemical Amount, and Stoichiometric Amount|journal=Journal of Chemical Education|volume=93|issue=4|pages=583–86|year=2016|last1=Giunta|first1=Carmen J.|bibcode=2016JChEd..93..583G|doi-access=free}}</ref> rather than the number of particles. There are proposals to replace "amount of substance" with more easily-distinguishable terms, such as '''enplethy'''<ref name="Cohen">{{GreenBook3rd|page=4}}</ref>  and '''stoichiometric amount'''.<ref name="Giunta"/>

The [[IUPAC]] recommends that "amount of substance" should be used instead of "number of moles", just as the quantity [[mass]] should not be called "number of kilograms".<ref name="Cohen"/>

== Nature of the particles ==
{{see also|Mole (unit)#Nature of the entities}}
{{wiktionary|amount of substance}}
To avoid ambiguity, the nature of the particles should be specified in any measurement of the amount of substance: thus, a sample of 1&nbsp;mol ''of molecules'' of [[oxygen]] ({{chem|O|2}}) has a mass of about 32 grams, whereas a sample of 1&nbsp;mol ''of atoms'' of oxygen ({{chem|O}}) has a mass of about 16 grams.<ref name="GoldBook">{{GoldBookRef|title=amount of substance, ''n''|file=A00297}}</ref><ref>{{GreenBook3rd|page=53-54}}</ref>

== Derived quantities ==
=== Molar quantities (per mole) <span class="anchor" id="Molar quantities"></span><span class="anchor" id="Per mole"></span> ===
[[Image:Mass versus moles of iron vs gold.svg|thumb|300px|A diagram comparing [[Mole (unit)|moles]] and [[Molar mass|molar masses]] of [[iron]] and [[gold]] samples that have equal [[Mass|masses]]]]
{{see also|Intensive and extensive properties#Molar properties}}

The quotient of some [[extensive property|extensive]] physical quantity of a homogeneous sample by its amount of substance is an [[intensive property]] of the substance, usually named by the prefix "molar" or the suffix "per mole".<ref name="molar">{{GreenBook3rd|page=6}}</ref>

For example, the quotient of the mass of a sample by its amount of substance is its [[molar mass]], for which the SI unit kilogram per mole or gram per mole may be used. This is about 18.015&nbsp;g/mol for water, and 55.845&nbsp;g/mol for [[iron]].  Similarly for volume, one gets the [[molar volume]], which is about 18.069 [[millilitre]]s per mole for liquid water and 7.092&nbsp;mL/mol for iron at room temperature.  From the [[heat capacity]], one gets the [[molar heat capacity]], which is about 75.385&nbsp;[[joule|J]]/([[kelvin|K]]⋅mol) for water and about 25.10&nbsp;J/(K⋅mol) for iron.

==== Molar mass ====
The [[molar mass]] (<math>M</math>) of a substance is the ratio of the [[mass]] (<math>m</math>) of a sample of that substance to its amount of substance (<math>n</math>): <math>M=m/n</math>. The amount of substance is given as the number of moles in the sample. For most practical purposes, the numerical value of the molar mass in [[Gram|grams]] per mole is the same as that of the mean mass of one molecule or formula unit of the substance in [[dalton (unit)|daltons]], as the mole was historically defined such that the [[molar mass constant]] was exactly 1&nbsp;g/mol. Thus, given the molecular mass or formula mass in daltons, the same number in grams gives an amount very close to one mole of the substance. For example, the average molecular mass of water is about 18.015&nbsp;Da and the molar mass of water is about 18.015&nbsp;g/mol. This allows for accurate determination of the amount in moles of a substance by measuring its mass and dividing by the molar mass of the compound: <math>n=m/M</math>.<ref name="BIPMrealise">[[International Bureau of Weights and Measures]]. [http://www.bipm.org/utils/en/pdf/SIApp2_mol_en.pdf Realising the mole] {{webarchive|url=https://web.archive.org/web/20080829154405/http://www.bipm.org/utils/en/pdf/SIApp2_mol_en.pdf|date=2008-08-29}}. Retrieved 25 September 2008.</ref> For example, 100&nbsp;g of water is about 5.551&nbsp;mol of water. Other methods of determining the amount of substance include the use of the [[molar volume]] or the measurement of [[electric charge]].<ref name=BIPMrealise/>

The molar mass of a substance depends not only on its [[molecular formula]], but also on the distribution of [[isotopes]] of each chemical element present in it. For example, the molar mass of [[calcium-40]] is {{val|39.96259098|(22)|u=g/mol}}, whereas the molar mass of [[calcium-42]] is {{val|41.95861801|(27)|u=g/mol}}, and of [[calcium]] with the normal isotopic mix is {{val|40.078|(4)|u=g/mol}}.

=== Amount (molar) concentration (moles per liter) ===
Another important derived quantity is the [[molar concentration]] (<math>c</math>) (also called ''amount of substance concentration'',<ref>{{GoldBookRef|title=amount-of-substance concentration|file=A00298}}</ref> ''amount concentration'', or ''substance concentration'',<ref>{{cite journal | author = International Union of Pure and Applied Chemistry | year = 1996 | title = Glossary of Terms in Quantities and Units in Clinical Chemistry | url = http://www.iupac.org/publications/pac/1996/pdf/6804x0957.pdf | journal = [[Pure and Applied Chemistry|Pure Appl. Chem.]] | volume = 68 | pages = 957–1000 | doi=10.1351/pac199668040957| s2cid = 95196393 | author-link = International Union of Pure and Applied Chemistry }}</ref> especially in [[clinical chemistry]]), defined as the amount in moles (<math>n</math>) of a specific substance (solute in a solution or component of a mixture), divided by the volume (<math>V</math>) of the solution or mixture: <math>c=n/V</math>.

The standard SI unit of this quantity is mol/[[Cubic metre|m<sup>3</sup>]], although more practical units are commonly used, such as mole per [[Litre|liter]] (mol/L, equivalent to mol/dm<sup>3</sup>).  For example, the amount concentration of [[sodium chloride]] in ocean water is typically about 0.599&nbsp;mol/L.

The denominator is the volume of the solution, not of the solvent. Thus, for example, one liter of standard [[vodka]] contains about 0.40 L of [[ethanol]] (315 g, 6.85&nbsp;mol) and 0.60 L of water. The amount concentration of ethanol is therefore (6.85&nbsp;mol of ethanol)/(1 L of vodka) = 6.85&nbsp;mol/L, not (6.85&nbsp;mol of ethanol)/(0.60 L of water), which would be 11.4&nbsp;mol/L.

In chemistry, it is customary to read the unit "mol/L" as '''[[molar (unit)|molar]]''', and denote it by the symbol "M" (both following the numeric value). Thus, for example, each liter of a "0.5 molar" or "0.5 M" solution of [[urea]] ({{chem|CH|4|N|2|O}}) in water contains 0.5 moles of that molecule.  By extension, the amount concentration is also commonly called the '''molarity''' of the substance of interest in the solution.  However, as of May 2007, these terms and symbols are not condoned by IUPAC.<ref>{{GreenBook3rd|page=48&nbsp;(n.&nbsp;15)}}</ref>

This quantity should not be confused with the [[mass concentration (chemistry)|mass concentration]], which is the mass of the substance of interest divided by the volume of the solution (about 35 g/L for sodium chloride in ocean water).

=== Amount (molar) fraction (moles per mole) ===
Confusingly, the amount (molar) concentration should also be distinguished from the [[molar fraction]] (also called [[mole fraction]] or [[amount fraction]]) of a substance in a mixture (such as a solution), which is the number of moles of the compound in one sample of the mixture, divided by the total number of moles of all components. For example, if 20&nbsp;g of {{chem|NaCl}} is dissolved in 100&nbsp;g of water, the amounts of the two substances in the solution will be (20&nbsp;g)/(58.443&nbsp;g/mol) = 0.34221&nbsp;mol and (100&nbsp;g)/(18.015&nbsp;g/mol) = 5.5509&nbsp;mol, respectively; and the molar fraction of {{chem|NaCl}} will be {{nowrap|1=0.34221/(0.34221 + 5.5509) = 0.05807}}.

In a mixture of gases, the [[partial pressure]] of each component is proportional to its molar fraction.

== History ==
The [[Alchemy|alchemists]], and especially the early [[metallurgist]]s, probably had some notion of amount of substance, but there are no surviving records of any generalization of the idea beyond a set of recipes. In 1758, [[Mikhail Lomonosov]] questioned the idea that mass was the only measure of the quantity of matter,<ref>{{Cite book | last = Lomonosov | first = Mikhail | author-link = Mikhail Lomonosov | year = 1970 | contribution = On the Relation of the Amount of Material and Weight | editor-first = Henry M. | editor-last = Leicester | title = Mikhail Vasil'evich Lomonosov on the Corpuscular Theory | contribution-url=//archive.org/stream/mikhailvasilevic017733mbp#page/n239/mode/2up | location = Cambridge, MA | publisher = Harvard University Press | pages = 224–33 |via=[[Internet Archive]]}}</ref> but he did so only in relation to his theories on [[gravitation]]. The development of the concept of amount of substance was coincidental with, and vital to, the birth of modern chemistry.
* '''1777''': [[Carl Friedrich Wenzel|Wenzel]] publishes ''Lessons on Affinity'', in which he demonstrates that the proportions of the "base component" and the "acid component" ([[cation]] and [[anion]] in modern terminology) remain the same during reactions between two neutral [[Salt (chemistry)|salts]].<ref name="Larousse">{{Cite journal | title = Atome | journal = [[Grand dictionnaire universel du XIXe siècle]] | publisher = [[Pierre Larousse]] | location = Paris | year = 1866 | volume = 1 | pages = 868–73}}. {{in lang|fr}}</ref>
* '''1789''': [[Antoine Lavoisier|Lavoisier]] publishes ''Treatise of Elementary Chemistry'', introducing the concept of a [[chemical element]] and clarifying the [[Law of conservation of mass]] for chemical reactions.<ref>{{cite book | first = Antoine | last = Lavoisier | year = 1789 | title = Traité élémentaire de chimie, présenté dans un ordre nouveau et d'après les découvertes modernes | url = http://gallica.bnf.fr/ark:/12148/bpt6k3930k.table | location = Paris | publisher = Chez Cuchet}}. {{in lang|fr}}</ref>
* '''1792''': [[Jeremias Benjamin Richter|Richter]] publishes the first volume of ''Stoichiometry or the Art of Measuring the Chemical Elements'' (publication of subsequent volumes continues until 1802). The term "[[stoichiometry]]" is used for the first time. The first tables of [[equivalent weight]]s are published for [[acid–base reaction]]s. Richter also notes that, for a given acid, the equivalent mass of the acid is proportional to the mass of oxygen in the base.<ref name="Larousse" />
* '''1794''': [[Joseph Proust|Proust's]] [[Law of definite proportions]] generalizes the concept of equivalent weights to all types of chemical reaction, not simply acid–base reactions.<ref name="Larousse" />
* '''1805''': [[John Dalton|Dalton]] publishes his first paper on modern [[atomic theory]], including a "Table of the relative weights of the ultimate particles of gaseous and other bodies".<ref>{{cite journal | first = John | last = Dalton | author-link= John Dalton | title = On the Absorption of Gases by Water and Other Liquids | url = http://web.lemoyne.edu/~giunta/dalton52.html | journal = Memoirs of the Literary and Philosophical Society of Manchester |series=2nd Series | volume = 1 | year = 1805 | pages = 271–87}}</ref>
*:The concept of atoms raised the question of their weight. While many were skeptical about the reality of atoms, chemists quickly found atomic weights to be an invaluable tool in expressing stoichiometric relationships.
* '''1808''': Publication of Dalton's ''A New System of Chemical Philosophy'', containing the first table of [[atomic weight]]s (based on H = 1).<ref>{{cite book | first = John | last = Dalton | author-link = John Dalton | title = A New System of Chemical Philosophy | url = https://archive.org/details/newsystemofchemi01daltuoft | location = Manchester | year = 1808| publisher = London }}</ref>
* '''1809''': [[Joseph Louis Gay-Lussac|Gay-Lussac's]] [[Gay-Lussac's law|Law of combining volumes]], stating an integer relationship between the volumes of reactants and products in the chemical reactions of gases.<ref>{{cite journal | first = Joseph Louis | last = Gay-Lussac | author-link = Joseph Louis Gay-Lussac | title = Memoire sur la combinaison des substances gazeuses, les unes avec les autres | journal = Mémoires de la Société d'Arcueil | year = 1809 | volume = 2 | pages = 207}} [http://web.lemoyne.edu/~giunta/gaylussac.html English translation].</ref>
* '''1811''': [[Amedeo Avogadro|Avogadro]] hypothesizes that equal volumes of different gases (at same temperature and pressure) contain equal numbers of particles, now known as [[Avogadro's law]].<ref>{{cite journal | first = Amedeo | last = Avogadro | author-link = Amedeo Avogadro | title = Essai d'une maniere de determiner les masses relatives des molecules elementaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons | journal = Journal de Physique | year = 1811 | volume = 73 | pages = 58–76}} [http://web.lemoyne.edu/~giunta/avogadro.html English translation].</ref>
* '''1813/1814''': [[Jöns Jakob Berzelius|Berzelius]] publishes the first of several tables of atomic weights based on the scale of ''m''(O) = 100.<ref name="Larousse" /><ref>Excerpts from Berzelius' essay: [http://web.lemoyne.edu/~giunta/berzatom.html Part II]; [http://web.lemoyne.edu/~giunta/berzelius.html Part III].</ref><ref>Berzelius' first atomic weight measurements were published in Swedish in 1810: {{cite journal | last = Hisinger | first = W. |author2=Berzelius, J.J. |author-link2=Jöns Jakob Berzelius  |title = Forsok rorande de bestamda proportioner, havari den oorganiska naturens bestandsdelar finnas forenada | journal = Afh. Fys., Kemi Mineral. | volume = 3 | pages = 162 | year = 1810}}</ref>
* '''1815''': [[William Prout|Prout]] publishes his [[Prout's hypothesis|hypothesis]] that all atomic weights are integer multiple of the atomic weight of hydrogen.<ref>{{cite journal | first = William | last = Prout | author-link = William Prout | year = 1815 | title = On the relation between the specific gravities of bodies in their gaseous state and the weights of their atoms | url = http://web.lemoyne.edu/~giunta/PROUT.HTML | journal = [[Annals of Philosophy]] | volume = 6 | pages = 321–30}}</ref> The hypothesis is later abandoned given the observed atomic weight of [[chlorine]] (approx.&nbsp;35.5 relative to hydrogen).
* '''1819''': [[Dulong–Petit law]] relating the atomic weight of a solid element to its [[specific heat capacity]].<ref>{{cite journal | last = Petit | first = Alexis Thérèse | author-link = Alexis Thérèse Petit |author2=Dulong, Pierre-Louis |author-link2=Pierre Louis Dulong  | title = Recherches sur quelques points importants de la Théorie de la Chaleur | journal = [[Annales de Chimie et de Physique]] | volume = 10 | pages = 395–413 | year = 1819}} [http://web.lemoyne.edu/~giunta/PETIT.html English translation]</ref>
* '''1819''': [[Eilhard Mitscherlich|Mitscherlich's]] work on [[crystal]] [[isomorphism]] allows many [[chemical formula]]e to be clarified, resolving several ambiguities in the calculation of atomic weights.<ref name="Larousse" />
* '''1834''': [[Benoît Paul Émile Clapeyron|Clapeyron]] states the ideal gas law.<ref>{{cite journal | last = Clapeyron | first = Émile | author-link = Benoît Paul Émile Clapeyron | year = 1834 | title = Puissance motrice de la chaleur | journal = Journal de l'École Royale Polytechnique | issue = 23 | volume = 14 | pages = 153–90}}</ref>
*:The [[ideal gas law]] was the first to be discovered of many relationships between the number of atoms or molecules in a system and other physical properties of the system, apart from its mass. However, this was not sufficient to convince all scientists of the existence of atoms and molecules, many considered it simply being a useful tool for calculation.
* '''1834''': [[Michael Faraday|Faraday]] states his [[Faraday's laws of electrolysis|Laws of electrolysis]], in particular that "the chemical decomposing action of a current is ''constant for a constant quantity of electricity''".<ref>{{cite journal | first = Michael | last = Faraday | author-link = Michael Faraday | year = 1834 | title = On Electrical Decomposition | url = http://www.chemteam.info/Chem-History/Faraday-electrochem.html | journal = Philosophical Transactions of the Royal Society | doi = 10.1098/rstl.1834.0008 | volume=124 | pages=77–122| s2cid = 116224057 }}</ref>
* '''1856''': [[August Krönig|Krönig]] derives the ideal gas law from [[kinetic theory of gases|kinetic theory]].<ref>{{cite journal | last = Krönig | first = August | author-link = August Krönig | title = Grundzüge einer Theorie der Gase | journal = Annalen der Physik | volume = 99 | pages =315–22 | year = 1856 | url = http://gallica.bnf.fr/ark:/12148/bpt6k15184h/f327.table | doi = 10.1002/andp.18561751008 | bibcode=1856AnP...175..315K | issue = 10}}</ref> [[Rudolf Clausius|Clausius]] publishes an independent derivation the following year.<ref>{{cite journal | last = Clausius | first = Rudolf | author-link = Rudolf Clausius | title = Ueber die Art der Bewegung, welche wir Wärme nennen | journal = Annalen der Physik | volume = 176 | pages =353–79 | year = 1857 | url = http://gallica.bnf.fr/ark:/12148/bpt6k15185v/f371.table | doi = 10.1002/andp.18571760302 | bibcode=1857AnP...176..353C | issue = 3}}</ref>
* '''1860''': The [[Karlsruhe Congress]] debates the relation between "physical molecules", "chemical molecules" and atoms, without reaching consensus.<ref>[[Charles-Adolphe Wurtz|Wurtz's]] [http://web.lemoyne.edu/~giunta/karlsruhe.html Account of the Sessions of the International Congress of Chemists in Karlsruhe, on 3, 4, and 5 September 1860].</ref>
* '''1865''': [[Johann Josef Loschmidt|Loschmidt]] makes the first estimate of the size of gas molecules and hence of number of molecules in a given volume of gas, now known as the [[Loschmidt constant]].<ref>{{cite journal | first = J. | last = Loschmidt | author-link = Johann Josef Loschmidt | title = Zur Grösse der Luftmoleküle | journal = Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien | volume = 52 | issue = 2 | pages = 395–413 | year =1865}} [http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html English translation] {{webarchive |url=https://web.archive.org/web/20060207130125/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html |date=February 7, 2006 }}.</ref>
* '''1886''': [[Jacobus Henricus van 't Hoff|van't Hoff]] demonstrates the similarities in behaviour between dilute solutions and ideal gases.
* '''1886''': [[Eugen Goldstein]] observes [[Anode ray|discrete particle ray]]s in gas discharges, laying the foundation of [[mass spectrometry]], a tool subsequently used to establish the masses of atoms and molecules.
* '''1887''': [[Svante Arrhenius|Arrhenius]] describes the dissociation of [[electrolyte]] in solution, resolving one of the problems in the study of colligative properties.<ref>{{cite journal |title=none| first = Svante | last = Arrhenius | author-link = Svante Arrhenius | journal = Zeitschrift für Physikalische Chemie | volume = 1 | pages = 631 | year = 1887}} [http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Arrhenius-dissociation.html English translation] {{Webarchive|url=https://web.archive.org/web/20090218052127/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Arrhenius-dissociation.html |date=2009-02-18 }}.</ref>
* '''1893''': First recorded use of the term ''mole'' to describe a unit of amount of substance by [[Wilhelm Ostwald|Ostwald]] in a university textbook.<ref>{{cite book | last = Ostwald | first = Wilhelm | author-link = Wilhelm Ostwald | year = 1893 | title = Hand- und Hilfsbuch zur ausführung physiko-chemischer Messungen | publisher = W. Engelmann | url = https://archive.org/details/handundhilfsbuc00ostwgoog | location = Leipzig}}</ref>
* '''1897''': First recorded use of the term ''mole'' in English.<ref>{{cite book | last =Helm | first = Georg | title = The Principles of Mathematical Chemistry: The Energetics of Chemical Phenomena | url =https://archive.org/details/principlesofmath00helmrich | others = (Transl. Livingston, J.; Morgan, R.) | location = New York | publisher = Wiley | year = 1897 | pages = [https://archive.org/details/principlesofmath00helmrich/page/n21/mode/2up 6]}}</ref>
* By the '''turn of the twentieth century''', the concept of atomic and molecular entities was generally accepted, but many questions remained, not least the size of atoms and their number in a given sample. The concurrent development of [[mass spectrometry]], starting in 1886, supported the concept of atomic and molecular mass and provided a tool of direct relative measurement.
* '''1905''': [[Albert Einstein|Einstein's]] paper on [[Brownian motion]] dispels any last doubts on the physical reality of atoms, and opens the way for an accurate determination of their mass.<ref>{{Cite journal | last=Einstein | first = Albert | author-link = Albert Einstein | title = Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen | journal = Annalen der Physik | volume = 17 | pages =549–60| year = 1905 | doi=10.1002/andp.19053220806 | bibcode=1905AnP...322..549E | issue=8| url = http://sedici.unlp.edu.ar/handle/10915/2785 | doi-access = free }}</ref>
* '''1909''': [[Jean Baptiste Perrin|Perrin]] coins the name [[Avogadro constant]] and estimates its value.<ref>{{cite journal | first = Jean | last = Perrin | author-link = Jean Baptiste Perrin | title = Mouvement brownien et réalité moléculaire | journal = [[Annales de Chimie et de Physique]] |series=8{{sup|e}} Série | volume = 18 | pages = 1–114 | year = 1909}} [http://web.lemoyne.edu/~giunta/perrin.html Extract in English, translation by Frederick Soddy].</ref>
* '''1913''': Discovery of [[isotope]]s of non-radioactive elements by [[Frederick Soddy|Soddy]]<ref>{{cite journal | last = Soddy | first = Frederick | author-link = Frederick Soddy | title = The Radio-elements and the Periodic Law | url = http://web.lemoyne.edu/~giunta/soddycn.html | journal = Chemical News | volume = 107 | pages = 97–99 | year = 1913}}</ref> and [[J. J. Thomson|Thomson]].<ref>{{cite journal | last = Thomson | first = J.J. | author-link = J. J. Thomson | title = Rays of positive electricity | url = http://web.lemoyne.edu/~giunta/canal.html | journal = Proceedings of the Royal Society A | volume = 89 | pages = 1–20 | year = 1913 | doi = 10.1098/rspa.1913.0057 | bibcode=1913RSPSA..89....1T | issue = 607| doi-access = free }}</ref>
* '''1914''': [[Theodore William Richards|Richards]] receives the Nobel Prize in Chemistry for "his determinations of the atomic weight of a large number of elements".<ref>Söderbaum, H.G. (November 11, 1915). ''[http://nobelprize.org/nobel_prizes/chemistry/laureates/1914/press.html Statement regarding the 1914 Nobel Prize in Chemistry]''.</ref>
* '''1920''': [[Francis William Aston|Aston]] proposes the [[whole number rule]], an updated version of [[Prout's hypothesis]].<ref>{{cite journal | last = Aston | first = Francis W. | author-link = Francis William Aston | year = 1920 | title = The constitution of atmospheric neon | journal = Philosophical Magazine | volume = 39 | issue = 6 | pages = 449–55 | doi=10.1080/14786440408636058| url = https://zenodo.org/record/1430720 }}</ref>
* '''1921''': Soddy receives the Nobel Prize in Chemistry "for his work on the chemistry of radioactive substances and investigations into isotopes".<ref>Söderbaum, H.G. (December 10, 1921). ''[http://nobelprize.org/nobel_prizes/chemistry/laureates/1921/press.html Presentation Speech for the 1921 Nobel Prize in Chemistry]''.</ref>
* '''1922''': Aston receives the Nobel Prize in Chemistry "for his discovery of isotopes in a large number of non-radioactive elements, and for his whole-number rule".<ref>Söderbaum, H.G. (December 10, 1922). ''[http://nobelprize.org/nobel_prizes/chemistry/laureates/1922/press.html Presentation Speech for the 1922 Nobel Prize in Chemistry]''.</ref>
* '''1926''': Perrin receives the [[Nobel Prize in Physics]], in part for his work in measuring the Avogadro constant.<ref>[[Carl Wilhelm Oseen|Oseen, C.W.]] (December 10, 1926). ''[http://nobelprize.org/nobel_prizes/chemistry/laureates/1926/press.html Presentation Speech for the 1926 Nobel Prize in Physics]''.</ref>
* '''1959'''/'''1960''': Unified atomic mass unit scale based on ''m''({{sup|12}}C) = 12&nbsp;u adopted by [[IUPAP]] and [[IUPAC]].<ref name="Holden">{{cite journal | last = Holden | first = Norman E. | url = http://www.iupac.org/publications/ci/2004/2601/1_holden.html | journal = Chemistry International | year = 2004 | issue = 1 | title = Atomic Weights and the International Committee – A Historical Review | volume = 26 | pages = 4–7}}</ref>
* '''1968''': The mole is recommended for inclusion in the [[International System of Units]] (SI) by the [[International Committee for Weights and Measures]] (CIPM).<ref name="SI">{{SIbrochure8th|pages=114–15}}</ref>
* '''1972''': The mole is approved as the [[SI base unit]] of amount of substance.<ref name="SI" />
* '''2019''': The mole is redefined in the SI as "the amount of substance of a system that contains {{val|6.02214076|e=23}} specified elementary entities".<ref name=bipm9th/>

== See also ==
* [[International System of Quantities]]
* [[Quantity of matter]]

== References ==
{{reflist|30em}}

{{Mole concepts}}
{{SI base quantities}}
{{Authority control}}

[[Category:Amount of substance| ]]
[[Category:SI base quantities]]